Combined implicit-explicit algorithms for non-linear structural dynamics

To solve fast dynamic problems, an explicit method is the most adapted. But for slower dynamics, an implicit method is more stable. The industrial problems are governed by high frequency (impact, ...) during short time intervals and slower dynamics (spring-back, ...) during other time intervals. The optimal solution is then to have both implicit algorithm and explicit methods readily available in the same code and to be able to switch automatically from one to another. Criteria that decide when to shift from a method to another have been developed here. Implicit balanced restarting conditions that annihilate numerical oscillations resulting for an explicit calculation are also proposed.